The invention relates to a method for correcting at least one portion of a spectrum, in particular a Raman spectrum, by eliminating a baseline which is due to a perturbing spectrum, in particular due to a fluorescence spectrum, superimposed on the spectrum.
The invention furthermore relates to a device for carrying out the method, as well as to a spectrometer device having a spectrometer, and to a computer-readable data medium on which a program which can carry out the method mentioned at the outset is stored.
Although the method according to the invention is described in the present description especially with reference to the example of correcting a Raman spectrum by eliminating a baseline which is due to a fluorescence spectrum superimposed on the spectrum, the method according to the invention can be used quite generally for correcting spectra on which an undesirable perturbing spectrum, which imposes an undesirable baseline on the desired spectrum, is superimposed.
Raman spectroscopy is an extensively used method for studying samples, for example biological substances.
An ideal Raman spectrum has Raman bands which lie on a straight baseline. A broadband perturbing spectrum or background spectrum, generally a fluorescence spectrum, is unfortunately often superimposed on Raman spectra. This perturbing spectrum may have very different curve profiles. In any event, a perturbing spectrum falsifies the desired Raman spectrum and makes it difficult to evaluate. Various methods have therefore already been employed in order to eliminate the perturbing spectrum from the Raman spectrum.
One method is to directly avoid a perturbing spectrum, such as a fluorescence spectrum, on the equipment side when recording the spectrum. However, these methods require modifications to the spectrometer and therefore increase the equipment outlay. Such equipment measures furthermore need to be readapted from sample to sample, which also leads to an increase in the time outlay for recording a spectrum besides increasing the equipment outlay.
Other methods, which do not entail the aforementioned disadvantages, consist in computationally eliminating the perturbing spectrum from the desired spectrum after recording the spectrum.
The US article by CHAD A. LIEBER and ANITA MAHADEVAN-JANSEN “Automated Method for Subtraction of Fluorescence from Biological Raman Spectra” published in APPLIED SPECTROSCOPY, 2003, pages 1362 to 1367, describes various methods for subtracting a fluorescence spectrum from a Raman spectrum. One of the methods described there consists in fitting a polynomial to the undesirable baseline of the recorded original or raw spectrum, which unfortunately makes it difficult to automate the correction method, requires a plurality of interventions by the user and is time-consuming, and furthermore needs to be readapted to the possible different curve profiles of perturbing spectra from case to case. A procedure described there as suitable for automation of the correction method is therefore a variant of the method of fitting the undesirable baseline by a polynomial, which operates with the aid of the least-squares method.
Automated use of the function, however, is virtually impossible since it is necessary for the degree of the polynomial to be established by the user before the calculation.
A better approach than this, on which the present invention is based, consists in finding a convex envelope of the spectrum and subtracting the convex part of the envelope lying below the spectrum from the spectrum in the portion to be corrected.
When a convex envelope of the spectrum is determined and the part of the convex envelope lying below the spectrum is subtracted from the spectrum, this method is also referred to as “rubber band” correction. Illustratively, this method can be interpreted as a rubber band, whose ends are fixed to the ends of the spectrum or the at least one portion of the spectrum which is to be corrected, being wrapped around the curve profile of the spectrum from below. The rubber band then fits itself against the curve profile of the spectrum. As seen from the x axis or from below, the rubber band assumes a convex polynomial configuration which corresponds to the undesirable baseline to be subtracted from the spectrum. If this is then taken away from the spectrum, the desired spectrum with a corrected baseline is obtained.
The “rubber band” correction method, however, does not lead to the desired elimination of the perturbing spectrum when it has a curve profile which comprises not only convex regions but also concave regions. Again illustratively using the example of the aforementioned rubber band, this means that the rubber band does not enter the concave regions of the perturbing spectrum, so that these concave regions are still present in the corrected Raman spectrum after subtracting the convex part of the envelope lying below the spectrum, which however continues to falsify the Raman spectrum.
There is therefore still a need for an improved method of correcting a spectrum.